I entered NJ UI/HC/WD info when loading my W2 info (box 14) but it didn't include this value in total state paxes paid as only shows what I loaded in my W2 (box 17).

While those box 14 taxes (UI/HC/WD) can be deductible on your federal Schedule A if you are itemizing your deductions this year (they show as state mandatory taxes), they are not factored into your state income taxes paid for your return and state refund purposes.  They go to fund specific state programs.

If you aren't seeing them included in your Schedule A, make sure that you are eligible to itemize your deductions this year (since the standard deduction was double, many people no longer qualify to itemize) and make sure you have selected the appropriate menu option in box 14 (there should be a drop down box where you can select NJ UI/HC/WD)